The product rule and the quotient rule are a dynamic duo of differentiation problems. The quotient rule is actually the product rule in disguise and is used when differentiating a fraction the quotient rule states that for two functions, u and v, see if you can use the product rule and the chain rule on y uv1 to derive this formula. Differentiate using the product and quotient rules. For practice problems using the product rule and chain rule, see the chain rule. Students will practice differentiation of common functions using the product and quotient rules they dont need to apply the chain rule. By using these rules along with the power rule and some basic formulas see chapter 4, you can find the derivatives of most of the singlevariable functions you encounter in calculus. Then now apply the product rule in the first part of the numerator. This lesson contains the following essential knowledge ek concepts for the ap calculus course. Examples of such functions are x2 sinx, 5xlog x, and ex cosx.
Calculus i exam 2 supplemental problems miscillanious problems 28. In some cases it might be advantageous to simplifyrewrite first. Find the first derivative of the following functions. This is going to be a rule which is very important to practice with over and over again. Product rule, quotient rule jj ii product rule, quotient rule. Reason for the product rule the product rule must be utilized when the derivative of the product of two functions is to be taken.
More practice more practice using all the derivative rules. In what follows we explore why this is the case, what the product and quotient rules actually say, and work to expand our repertoire of functions we can easily differentiate. Derivative worksheets include practice handouts based on power rule, product rule, quotient rule, exponents, logarithms, trigonometric angles, hyperbolic functions, implicit differentiation and more. Here is a set of practice problems to accompany the product and quotient rule section of the derivatives chapter of the notes for paul dawkins calculus i course at lamar university. This calculus video tutorial explains the concept of implicit differentiation and how to use it to differentiate trig functions using the product rule, quotient rule fractions, and chain rule. Differentiate using the product and quotient rules practice. Exponents and the product, quotient, and power rules. The quotient rule in words the quotient rule says that the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. In calculus, the chain rule is a formula for computing the. The product rule states that if u and v are both functions of x and y is their product, then the derivative of y is given by. Problem solving use acquired knowledge to solve product rule practice problems. It will take a bit of practice to make the use of the chain rule come naturallyit is. Product, quotient and chain rules at the beginning of the semester we discussed the fact that we can multiply and divide two functions to get a new function. Answers to chain rule practice 1 dy dx x x x x 2 dy dx x x x x 3 f x x x x.
Here is a set of practice problems to accompany the product and quotient rule section of the derivatives chapter of the notes for paul dawkins. Before using the chain rule, lets multiply this out and then take the derivative. The next two examples illustrate functional and leibniz methods of attacking the same problem using the chain rule. R b2n0w1s3 s pknuyt yaj fs ho gfrtowgadrten hlyl hcb. Click here for an overview of all the eks in this course. A ball is thrown into the air and its height hin meters after tseconds is given by the function ht.
In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. The product, quotient and chain rules tell us how to differentiate in these three situations. Fortunately, we can develop a small collection of examples and rules that allow us. The question then becomes how do we take the derivative of the product or quotient of two functions. Apply the power rule of derivative to solve these pdf worksheets.
If you are unsure how to use the product rule to di. Final quiz solutions to exercises solutions to quizzes the full range of these packages and some instructions, should they be required, can be obtained from our web page mathematics support materials. The students will form two circles, inner and outer, and will be combining expressions to practice the product rule and the quotient rule. Then apply the product rule in the first part of the numerator. This video tutorial outlines 4 key differentiation rules used in calculus, the power, product, quotient, and chain rules. Carry through algebra to show that these are all equal. G u pmaadqeh fwvihtbhm viwnufkiknrixtqe\ fcwawlochulyu\s. C n2s0c1h3 j dkju ntva p zs7oif ktdweanrder nlqljc n. It is important to notice that we cannot just take the product or quotient of the derivatives. Although there are many ways to write the final answer, we usually want all factors written with positive exponents, except possibly exponential terms. The product, quotient, and chain rules the questions. The quotient rule is derived from the product rule and the chain rule.
You can still go the long way on these problems and simplify by writing out all the factors and combining or. If you combine the chain rule with the derivative for the square root function, you get p u0 u0. Differentiate using the chain rule practice questions. Watch the video lecture chain, product and quotient rule. Product rule lets practice this by calculating the marginal revenue function.
Chain rule, and this is covered in another worksheet. Suppose a monopolist faced the inverse demand function 100. Find the equation of the line that passes through 1. Here are a set of practice problems for my calculus i notes. The next two examples illustrate functional and leibniz methods of attacking. The product and quotient rules university of plymouth. With chain rule problems, never use more than one derivative rule per step. Feb 20, 2016 this calculus video tutorial explains the concept of implicit differentiation and how to use it to differentiate trig functions using the product rule, quotient rule fractions, and chain rule. If you are viewing the pdf version of this document as opposed to viewing it on the web this document contains only the problems themselves and no solutions are included in this document. Before you tackle some practice problems using these rules, heres a. Derivatives of exponential and logarithm functions. Selection file type icon file name description size revision time user. Although the chain rule is no more complicated than the rest, its easier to misunderstand it, and it takes care to determine whether the chain rule or the product rule. While the derivative of a sum is the sum of the derivatives, it turns out that the rules for computing derivatives of products and quotients are more complicated.
While we do obviously have a quotient here, we also have a product in the numerator, so before we can make any progress in di. This activity combines socializing with working product rule and quotient rule problems, so both you and your students will be happy. Product rule, quotient rule, chain rule the product rule gives the formula for differentiating the product of two functions, and the quotient rule gives the formula for differentiating the quotient of two functions. Only in the next step do you multiply the outside derivative by the derivative of the inside stuff. The first worksheet has the students finding the first derivatives of 16 functions. Product rule, quotient rule, and chain rule tutorial.
The product and quotient rules mathematics libretexts. Exponents power rule quotient rule worksheets kiddy math. In this exercise, when you compute the derivative of xtanx, youll need the product rule since thats a product. The chain rule is one of the most important rules in this list because many function cans be thought of as functions of functions of functions of functions. Power rule chain rule product and quotient rule dana c. Only in the next step do you multiply the outside derivative by the derivative of the inside. Implicit differentiation explained product rule, quotient. Theyre very useful because the product rule gives you the derivatives for the product of two functions, and the quotient rule does the same for the quotient of two functions. Constant rule power rule product rule quotient rule list of rules examples of constant, power, product and quotient rules derivatives of trig functions higher order derivatives more practice note that you can use. Worksheet for product, quotient and chain rule practicefind dydx. In other words, when you do the derivative rule for the outermost function, dont touch the inside stuff.
Differentiation rules powerproductquotientchain youtube. Find an equation of the tangent line tothecuwe y x 3 when x 1. The product, quotient, and chain rules this chapter focuses on some of the major techniques needed to find the derivative. The quotient rule mctyquotient20091 a special rule, thequotientrule, exists for di. Find the derivatives of the functions in 14 using the quotient rule. Mar 18, 2020 selection file type icon file name description size revision time user. Practice di erentiation math 120 calculus i d joyce, fall 20 the rules of di erentiation are straightforward, but knowing when to use them and in what order takes practice. Rules practice with tables and derivative rules in symbolic form. Handout derivative chain rule powerchain rule a,b are constants.
Use proper notation and simplify your final answers. Apr 24, 2012 this video tutorial outlines 4 key differentiation rules used in calculus, the power, product, quotient, and chain rules. The chain rule mctychain20091 a special rule, thechainrule, exists for di. The product rule says that the derivative of a product of two functions is the. Here is a set of practice problems to accompany the chain rule section of the derivatives chapter of the notes for paul dawkins calculus i course at lamar university. Quotient rule practice find the derivatives of the following rational functions. This chapter focuses on some of the major techniques needed to find the derivative.
25 1345 353 878 1313 41 1303 1278 114 120 950 178 1201 952 860 1034 107 1209 1428 850 546 719 1039 965 304 344 1352 573 1013 1344 581